Synchrotron Radiation and Free Electron Lasers Gwyn P

Synchrotron Radiation and Free Electron Lasers Gwyn P. Williams Jefferson Lab 12000 Jefferson Avenue - MS 7 A Newport News, VA 23606 gwyn@mailaps. org UVa April 14, 2004 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Synchrotron Radiation and Free Electron Lasers This lecture is aimed at teaching the physics of the production of very bright light, from a user perspective, NOT an accelerator perspective. It is not a rigorous presentation of theory, although it will contain all the critical theoretical arguments and equations. But most importantly it bridges the gap between Krafft et al’s lectures and practical calculations of light output. See G. P. Williams, Rep. Prog. Phys. 69 310 -326, 2006 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

X-Ray Brightness Growth vs Time Compared with Computers Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

How do we make light? Light (electromagnetic waves) is made by waving an electron around. e light Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Radiation from Accelerated Electron - Power Electric field goes linearly in the electric charge and the acceleration - so intensity (power) goes like e 2 a 2 electron But dimensions of power are: field acceleration Now for an electric charge, force is e 2/L 2, so we can derive dimensions for e thus: So e 2 a 2 has dimensions of : ML 3 T-2 L 2 T-4 = ML 5 T-6 And if we divide by c 3, or L 3 T-3, we get ML 2 T-3. Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Radiation from Accelerated Electron - Power Also we note that radiation is emitted in only 2 out of 3 directions, so we have a 2/3 factor, yielding: Larmor’s Formula Noting that the dimensions of power are ML 2 T-3, and noting That M goes like gamma, L goes like 1/gamma and T goes like gamma in the moving frame, in the rest frame the relativistic version is : N. B. Radiated energy and elapsed time transform in the same manner under Lorentz transforms J/cm-1/electron Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Theory D. H. Tomboulian & P. L. Hartman, Phys. Rev. 102 1423 (1956) J. Schwinger, Phys. Rev. 75 1912 (1949) J. D. Jackson, Classical Electrodynamics, Wiley, NY 1975 H. Winick, Synchrotron Radiation Research, Chap. 2, Plenum Press 1980. K. J. Kim AIP Proceedings 184 565 (1989). S. L. Hulbert and G. P. , Williams, "Synchrotron radiation sources. " In Handbook of Optics: Classical, Vision, and X-Ray Optics, 2 nd ed. , vol. III, chap. 32. Michael Bass, Jay M. Enoch, Eric W. Van Stryland, and William L. Wolfe (eds. ). New York: Mc. Graw-Hill, , pp. 32. 1 --32. 20 (2001). C. A. Brau, Modern Problems in Classical Electrodynamics, Oxford University Press (2004). Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Radiation from Accelerated Electron – Spectrum Intensity e 2 Electric field electron(s) time Thomas Jefferson National Accelerator freq. (1/time) Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Radiation from Accelerated Electron – Emission Angle = mass / rest mass r is lab (receiving frame) t is transmitting frame So t = 900 transforms to ~1/ in the lab frame Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Synchrotron Radiation Generation - theory Jackson, Classical Electrodynamics, Wiley, NY 1975 where e is the charge of an electron, is the ratio of the velocity of the particle to the speed of light, n is a unit vector and (t) is the particle position. Kim has shown that one can re-write this to give the total flux emitted in practical units, per horizontal milliradian per ampere into a 0. 1% bandwidth (D / or DE/E), integrated over q. V as: F tot= 2. 547 x 10 13 E (Ge. V) I (A) G 1(y) where G 1(y) is the Bessel function: with and Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Bessel Functions!!! The function G 1(y) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Bessel Functions!!! can be shown to be equivalent to: V. Kostroun, Nucl. Instr. & Methods 172 371 (1980). Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Brightness is sometimes called brilliance, or spectral radiance. It has units of power per unit area per unit solid angle. Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Emitted Flux as Function of Vertical Angle parallel perpendicular to orbit plane Units: photons/sec/mrad. (horiz)/mrad. (vert)/amp/0. 1%bw = 1957 E(Ge. V) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Emitted Flux as Function of Vertical Angle Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Synchrotron Radiation Source at JLab Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Spectral Brightness Photons/sec/mm 2/mrad 2/0. 1% bandwidth Synchrotron Radiation Source Brightness compared with table-top Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Looking at some brightness numbers Standard x-ray tube is a 10 ke. V beam of 10 m. A. Power in the electron beam is 100 Watts. X-ray power is then at most ~ 1 watt. Solid angle of emission = 4 steradians Area of source = 1 mm 2 Brightness is 1 / (4 1) = 0. 08 watts/str/mm 2 Synchrotron is, say 3 Ge. V, at 300 m. A. Power in the beam is then 1000 Megawatts X-ray power is then about 10 Megawatts. Questions: What is gamma for this ring, how fast are the electrons going, and how many electrons are circulating in the ring assuming a circumference of 200 m? Solid angle of emission = 2 10 -3 steradians Area of source = 0. 1 mm 2 Brightness is 107 / (2 10 -3 0. 1) = 1. 6 1010 watts/str/mm 2 Ratio of synchrotron / x-ray tube = 2 1011 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Synchrotron Radiation and Free Electron Lasers Up to this point we have assumed that each electron emitted independently within the bunch. Now we are going to advance considerably into a new regime in which electrons are going to radiate coherently, meaning that their electric fields will be in phase with each other. Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

How do we make light more powerful? 2 elight 4 times the power!!! e is charge on electron a is acceleration c is speed of light is relativistic mass increase Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Radiation from Accelerated Electron – Spectrum Intensity e 2 Electric field electron(s) time Thomas Jefferson National Accelerator freq. (1/time) Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Radiation from Accelerated Electrons – Spectrum Electric field E/N Intensity E 2 electron(s) time N super-radiant enhancement freq. (1/time) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Radiation from Accelerated Electrons - physics Statistics of an electron bunch in a storage ring Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Coherent Synchrotron Radiation Generation - theory Jackson, Classical Electrodynamics, Wiley, NY 1975 where e is the charge of an electron, is the ratio of the velocity of the particle to the speed of light, n is a unit vector and (t) is the particle position. Kim has shown that one can re-write this to give the total flux emitted in practical units, per horizontal milliradian per ampere into a 0. 1% bandwidth (Dl/l or DE/E), integrated over q. V as: F tot= 2. 547 x 10 13 E (Ge. V) I (A) G 1(y) where G 1(y) is the Bessel function: with and Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Coherent Synchrotron Radiation Generation - theory Jackson, Classical Electrodynamics, Wiley, NY 1975 f( ) is the form factor – the Fourier transform of the normalized longitudinal particle distribution within the bunch, S(z) REFERENCES S. L. Hulbert and G. P. Williams, Handbook of Optics: Classical, Vision, and X-Ray Optics, 2 nd ed. , vol. III. Bass, Michael, Enoch, Jay M. , Van Stryland, Eric W. and Wolfe William L. (eds. ). New York: Mc. Graw-Hill, 32. 1 -32. 20 (2001). S. Nodvick and D. S. Saxon, Suppression of coherent radiation by electrons in a synchrotron. Physical Review 96, 180 -184 (1954). Carol J. Hirschmugl, Michael Sagurton and Gwyn P. Williams, Multiparticle Coherence Calculations for Synchrotron Radiation Emission, Physical Review A 44, 1316, (1991). Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Synchrotron Radiation and Free Electron Lasers We have manipulated the electrons, now let’s manipulate their radiation paths. Instead of a single pass, let’s have an alternating series of magnets. electron(s) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

New Undulator at Jefferson Lab Wavelength Number of periods Gap 20 cm 12 ea. 26 mm Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Undulator and Free Electron Laser e- Ne- |NE( )|2 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Undulator and Free Electron Laser C. J. Hirschmugl, M. Sagurton and G. P. Williams, Physical Review A 44, 1316, (1991). Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Synchrotron Radiation Source Brightness compared with table-top including undulators and FELs Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Synchrotron Radiation Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Synchrotron Radiation Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Synchrotron Radiation - so what’s new here? radio-freq. cavity Showstopper……. Solution……. . 3 Energy Ge. V at. Recovery 100 m. A is 300 Megawatts!!!!! Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

First of a new generation of light source – The Energy Recovered Linac Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Jefferson Lab Free-electron Laser Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

The JLab 10 k. W IR FEL and 1 k. W UV FEL Presently under commissioning First light achieved on June 17, 2003 1000 TIMES BRIGHTER THAN ANY SUB-ps TABLE_TOP LASER Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Jefferson Lab FEL Superconducting Linac Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Superconducting Radio-Freq. Linac Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Undulator and Free Electron Laser C. J. Hirschmugl, M. Sagurton and G. P. Williams, Physical Review A 44, 1316, (1991). Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Coherent Synchrotron Radiation Generation - theory Jackson, Classical Electrodynamics, Wiley, NY 1975 2 nd. extra term Need to consider the term in the velocity, or the Coulomb or near-field term, particularly when R is small and gamma is small. REFERENCES R. A. Bosch, Nuclear Instr. & Methods A 431 320 (1999). M. Buess, G. L. Carr, O. Chubar, J. B. Murphy, I. Schmid & G. P. Williams “Exploring New Limits in Understanding The Emission of Light from Relativistic Electrons” in preparation for Nature. O. Chubar, P. Elleaume, "Accurate And Efficient Computation Of Synchrotron Radiation In The Near Field Region", proc. of the EPAC 98 Conference, 22 -26 June 1998, p. 1177 -1179. Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Brightness of IR Sources JLab THz JLab FEL Table-top sub-ps lasers ns o r t o r h c Syn r a b lo G THz proof of principle: Carr, Martin, Mc. Kinney, Neil, Jordan & Williams Nature 420, 153 (2002) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy FEL proof of principle: Neil et al. Phys. Rev. Letts 84, 662 (2000)

The THz Gap Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

The Real THz Gap Electronics - radios Photonics – light bulbs Tom Crowe, UVa Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

October 2002 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

THz Expt and Calculation Diffraction losses ~ 20 Watts integrated Carr, Martin, Mc. Kinney, Neil, Jordan & Williams Nature 420, 153 (2002) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

THz Imaging A tooth cavity shows up clearly in red. Teraview Ltd. Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

THz Imaging Basal cell carcinoma shows malignancy in red. Teraview Ltd. Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Terahertz computerized tomography 3 cm Turkey Bone Test Object Ferguson et. al. Phys. Med. Biol. 47 3735 (2002) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Terahertz Imaging Clery, Science 297 763 (2002) Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Introduction High power* THz light is critical for communications, imaging and remote sensing. Jefferson Lab operates a 100 Watt average, Megawatt peak power broadband THz source. Implementation of the above has become possible only recently with advances in the laboratory, particularly combining modern ultra-fast lasers with superconductivity and relativity. We have established a user facility which is equipped for spectroscopy and imaging proof of principle experiments in this new arena. Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

JLab Terahertz Beam Extraction and Transport M 2 M 3 diamond window Shutter/viewer & camera M 1 V 1 M 1 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Terahertz Beamline Schematic with Optical Ray-tracing Funding start 7/2003 M 4 THz To User Facility F 3 60 x 60 mm 200 x 200 mm F 2 60 x 60 mm M 2 200 x 200 mm M 1 THz Generation Optical calculations by Oleg Chubar, Paul Dumas Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy Funding US Army NVL

JLab power permits large area imaging ~ m 2 Optical transport output in User Lab Real time image from IR Demo Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Coherent Synchrotron Radiation Effect of Pulse Length FWHM Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Coherent Synchrotron Radiation Effect of Pulse Charge Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Applications – proof of principle expts. Passive Image 30 c m 2. Military/Commercial (b) Remote Sensing, high spatial resolution, with active imaging 2 m 10. 2 met ers 10 meters Clery, Science 297 763 (2002) 0. 3 cm of a 10 cm radius sphere will be normal to the beam, which is 0. 1%. Calculations using antenna coupled bolometer sensitivities Indicate that about 100 W is required for this application Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

FEL Team at JLab This work supported by the Office of Naval Research, the Joint Technology Office, the Commonwealth of Virginia, the Air Force Research Laboratory, Army Night. Thomas Vision Lab, and by DOE Contract DE-AC 05 Jefferson National Accelerator Facility 84 ER 40150. Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Addendum, an Application - Protein Structure Carboxypeptidase -turn -sheet synchrotron scattering extended coil -helix Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy film

Application to Protein Crystallography Synchrotron Radiation Brightness is 107 / (2 10 -3 0. 1) = 1. 6 1010 watts/str/mm 2 How many photons can we shine on a 100 micron protein crystal? Throughput (étendue) is area angle, and let’s say we are limited by 5 milliradians of angle. Area angle = 0. 01 5 10 -3 = 2. 5 10 -7 mm 2 str Flux on sample is therefore 1. 6 1010 2. 5 10 -7 = 4000 watts However to get a good diffraction pattern, we need to monochromatize the beam, to get a bandwidth of, say, 0. 1%, making the power 4 watts. Question: How many photons is this at h = 10 ke. V and what is their wavelength? Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Answers to Questions: What is gamma for this ring, how fast are the electrons going, and how many electrons are circulating in the ring assuming a circumference of 200 m? Rest mass of electron is 0. 5 Me. V, so gamma is 3 109 / 0. 5 106 = 6000 From relativity: putting in numbers: v = 0. 999999986 c Last is a trick question, but 1 ampere is 1 coulomb per second, and each electron carries a charge of 1. 6 10 -19 coulombs, and that would make 0. 3 / 1. 6 10 -19 = 1. 9 1018 electrons. However, for a 200 meter circumference ring, the circulation time is 0. 66 microseconds, so each electron is used 1. 5 million times. So the actual number of electrons is 1. 9 1018 / 1. 5 106 = 1. 2 1012 Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Answers to Questions Question: How many photons is 4 watts at 10 ke. V? 1 e. V is the energy required to accelerate an electron through 1 e. V potential. 1 watt is 1 amp / second at 1 volt, so 1 e. V is 1. 6 10 -19 joules. If each photon carries 10 ke. V of energy, it carries 1. 6 10 -15 joules. Therefore the number of photons is 4 / 1. 6 10 -15 = 2. 5 1015 / second. and what is their wavelength? Energy = h , and c = lambda , so Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Conventional THz Sources - Auston Switch for producing THz light Sub-picosecond laser pulse THz pulse Si or Ga. As Auston, D. H. , Cheung, K. P. , Valdmanis, J. A. and Kleinman, D. A. , Phys. Rev. Letters 53 1555 -1558 (1984). Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy

Comparing Coherent THz Synchrotron and Conventional THz Sources a=acceleration c=vel. of light =mass/rest mass e- -> 40 Me. V ~100 V THz Ga. As fsec laser pulse Ga. As Thomas Jefferson National Accelerator Facility Operated by the Southeastern Universities Research Association for the U. S. Department of Energy THz